Apparatuses, methods, systems, and computer-readable media for fluid potential artifact correction in reagent delivery systems

ABSTRACT

A method for correcting nucleotide incorporation signals for fluid potential effects or disturbances arising in nucleic acid sequencing-by-synthesis includes: disposing a plurality of template polynucleotide strands in a plurality of defined spaces disposed on a sensor array, the template polynucleotide strands having a sequencing primer and a polymerase bound therewith; exposing the template polynucleotide strands to a series of flows of nucleotide species flowed through a fluid manifold, the fluid manifold comprising passages for flowing nucleotide species and a branch passage for flowing a solution, the branch passage comprising a reference electrode and a sensing electrode; obtaining a plurality of nucleotide incorporation signals corresponding to the plurality of defined spaces, the nucleotide incorporation signals having a signal intensity related to a number of nucleotide incorporations; and correcting at least some of the plurality of nucleotide incorporation signals for fluid potential effects or disturbances.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority under 35 U.S.C. §119(e) to U.S.Provisional Application No. 62/050,377, filed Sep. 15, 2014, entitled“Methods and Computer-Readable Media for Potential Artifact Correctionin Reagent Delivery Systems,” and to U.S. Provisional Application No.62/146,882, filed Apr. 13, 2015, entitled “Fluid Potential ArtifactCorrection,” the contents of the foregoing applications are incorporatedherein by reference in their entirety.

COPYRIGHT NOTICE

A portion of the disclosure of this patent document contains materialwhich is subject to copyright protection. The copyright owner has noobjection to the facsimile reproduction by anyone of the patent documentor the patent disclosure, as it appears in the Patent and TrademarkOffice patent file or records, but otherwise reserves all copyrightrights whatsoever.

FIELD OF THE DISCLOSURE

This application generally relates to apparatuses, methods, systems, andcomputer readable media for signal correction in reagent deliverysystems, and, more specifically, to apparatuses, methods, systems, andcomputer readable media for fluid potential artifact correction innucleic acid sequencing.

BACKGROUND

Semiconductor chips have been used to measure fluid potential. In someapplications, fluid flow is measured across a semiconductor chipincluding a sensor array having a plurality of rows and columns oftransistors. However, there are a number of obstacles in providingaccurate measurement based on current techniques.

Disturbances in electrolyte potential lead to measurement error, and maybe generated by the charging and discharging of parasitic capacitancesin the sensor array. Furthermore, these disturbances are not uniformacross the sensor array, as the disturbances are more common within rowsof the array and are more pronounced when switching between middle andtop/bottom rows of the array. Row select switching also couplesundesired signals into the fluid via a capacitance of columnmetallization. In addition to this stray column-to-fluid couplingcapacitance, measurement error may further be attributed toelectrostatic discharge that couples into the fluid, fluid resistance,leakage resistance, and the like. These effects are complicated by fluidflow across the semiconductor chip. In view of the above, it would beadvantageous to have a device for correcting these fluid potentialartifacts.

Various instruments or systems, which include one or more semiconductorchips, for sequencing nucleic acid sequences include reagent deliverysystems that use various fluidic communications to performsequencing-by-synthesis, including, for example, the Ion PGM™ and IonProton™ Sequencers using Ion Torrent™ sequencing technology (see, e.g.,U.S. Pat. No. 7,948,015 and U.S. Pat. Appl. Publ. Nos. 2010/0137143,2009/0026082, and 2010/0282617, which are all incorporated by referenceherein in their entirety). In order to increase accuracy of nucleic acidsequencing using these and other systems (such as, e.g.,sequencing-by-hybridization, sequencing-by-ligation, etc.) that deliverreagents via fluid, there is a need for new methods, systems, andcomputer readable media for correcting sequencing signals in thepresence of noise and/or artifacts that may arise due to various effectsor disturbances related to fluid carrying and/or delivering reagents.

SUMMARY OF THE DISCLOSURE

Embodiments disclose apparatuses, methods, systems, andcomputer-readable media for fluid potential artifact correction inreagent delivery systems. Further, embodiments disclose methods anddevices for measuring a reaction product. The following methods,systems, computer-readable media, and devices are exemplified in anumber of implementations, some of which are summarized below andthroughout the specification.

In one aspect, an apparatus for measuring a reaction product includes adevice including a flow cell in fluid communication with an electronicsensor. A plurality of reagent reservoirs are provided to include aplurality of reagents. A fluid manifold is in fluidic communication withthe plurality of reagent reservoirs. An outlet passage of the fluidmanifold is in fluid communication with the flow cell. A referenceelectrode provides a reference voltage to the electronic sensor throughfluid in the outlet passage and the flow cell. A sensor electrode is inelectrical communication with the fluid of the outlet passage and theflow cell.

In a related aspect, the fluid manifold further includes a branchpassage between the fluid manifold and the flow cell in fluidcommunication with the outlet passage. The reference electrode isdisposed in contact with fluid within the branch passage. The referenceelectrode is free of direct contact with any reagent of the plurality ofreagents when the any reagent flows through the outlet passage. Thesensor electrode is disposed in contact with the fluid within the branchpassage. The sensor electrode is disposed closer to the outlet passagethan the reference electrode. The sensor electrode is free of directcontact with any reagent of the plurality of reagents when the anyreagent flows through the outlet passage. A solution reservoir isprovided in fluid communication with the branch passage.

In a related aspect, the device further includes a second electronicsensor not in fluid communication with the flow cell, the secondelectronic sensor including a gate electrode, and an output from thesensor electrode in electrical communication with the gate electrode. Anamplifier is coupled to the sensor electrode and provides a referencevoltage offset to the sensor electrode. The electronic sensor includes afield effect transistor having a gate electrode. The electronic sensorincludes an ion sensitive field effect transistor.

In another aspect, an apparatus includes a flow cell including a fluidinlet and a fluid outlet. An array of electronic sensors arecooperatively engaged with the flow cell. Each of the electronic sensorsincludes a field effect transistor having a gate electrode. A firstsubset of the array of electronic sensors is exposed to a fluid withinthe flow cell. A second subset of the array of electronic sensors isfree of contact with the fluid within the flow cell. A sensor electrodeis in electrical communication with the first subset of the array ofelectronic sensors through fluid via the fluid inlet or the fluidoutlet. An output of the sensor electrode is in electrical communicationwith the gate electrodes of the field effect transistors of the secondsubset of the array of electronic sensors.

In a related aspect, the array of electronic sensors is arranged in rowsand columns. The second subset of the array of electronic sensorsincludes a column of electronic sensors. The output of the sensorelectrode is in electrical communication with the each electronic sensorwithin the column of electronic sensors of the second subset of thearray of electronic sensors. A fluid manifold is in fluid communicationwith a plurality of reagent reservoirs. The fluid manifold includes anoutlet passage in fluid communication with the fluid inlet. The sensorelectrode is in electrical communication with the second subset of thearray of electronic sensors through a solution via the outlet passage.

In a related aspect, a branch passage is provided between the fluidmanifold and the flow cell in fluid communication with the outletpassage. The sensor electrode is disposed in the branch passage. Thereference electrode is disposed in contact with fluid within the branchpassage. The reference electrode is free of direct contact with anyreagent of the plurality of reagents when the any reagent flows throughthe outlet passage. The sensor electrode is disposed in contact withfluid within the branch passage. The sensor electrode is disposed closerto the outlet passage than the reference electrode. The sensor electrodeis free of direct contact with any reagent of the plurality of reagentswhen the any reagent flows through the outlet passage.

In a related aspect, a solution reservoir is in fluid communication withthe branch passage. The plurality of reagent reservoirs include aplurality of reagents. A reference electrode provides a referencevoltage to the first subset of the array of electronic sensors through asolution via the fluid inlet or the fluid outlet. An array of wellsprovides fluid access to the gate electrodes of the field effecttransistors of the first subset of the array of electronic sensors. Anamplifier is disposed in electrical communication between the output ofthe sensor electrode and the gate electrodes of the field effecttransistors of the second subset of the array of electronic sensors. Thefield effect transistors of the first subset of the array of electronicsensors include ion sensitive field effect transistors.

In another aspect, a method of measuring a reaction product includesflowing a reagent solution into a flow cell. The reagent solution reactsto provide a reaction product. The flow cell is in fluid communicationwith a first electronic sensor. A response of the first electronicsensor to the reaction product is measured, and a response of a secondelectronic sensor is measured. The second electronic sensor is inelectrical communication with a sensor electrode in fluid communicationwith the flow cell. The second electronic sensor is not in fluidcommunication with the flow cell. The response of the first electronicsensor is adjusted based on the response of the second electronicsensor.

In a related aspect, a reference voltage is applied through a solutionin fluid communication with the flow cell in fluid communication withthe first electronic sensor. The reference voltage is applied by areference electrode. The first electronic sensor and the secondelectronic sensor include field effect transistors. The field effecttransistor of the first electronic sensor includes an ion sensitivefield effect transistor.

In a related aspect, a solution flows through the sensor electrode. Aresponse of the sensor electrode is measured through the solution. Theresponse of the sensor electrode is amplified. An offset to the measuredresponse of the sensor electrode is provided to center the measuredresponse relative to a reference voltage. The response of the firstelectronic sensor is adjusted by scaling and subtracting the response ofthe second electronic sensor.

In another aspect, a method of measuring a reaction product includesflowing a reagent solution into a flow cell. The reagent solution reactsto provide a reaction product. The flow cell is in fluid communicationwith an array of electronic sensors cooperatively engaged with the flowcell. A first subset of the array of electronic sensors is exposed tothe reagent solution within the flow cell. A second subset of the arrayof electronic sensors is free of contact with the reagent solution fluidwithin the flow cell. A response of the first subset of the array ofelectronic sensors to the reaction product is measured. A response ofthe second subset of the array of electronic sensors is measured. Thesecond subset of the array of electronic sensors is in electricalcommunication with a sensor electrode in fluid communication with theflow cell. The response of the first subset of the array of electronicsensors is adjusted based on the response of the second subset of thearray of electronic sensors.

In a related aspect, each of the electronic sensors includes a fieldeffect transistor having a gate electrode. The sensor electrode is inelectrical communication with the first subset of the array ofelectronic sensors through fluid. An output of the sensor electrode isin electrical communication with the gate electrodes of the field effecttransistors of the second subset of the array of electronic sensors. Thearray of electronic sensors is arranged in rows and columns. The secondsubset of the array of electronic sensors includes a column ofelectronic sensors. The output of the sensor electrode is in electricalcommunication with the each electronic sensor within the column ofelectronic sensors of the second subset of the array of electronicsensors. A reference voltage is provided through a solution in fluidcommunication with the flow cell in fluid communication with the firstsubset of the array of electronic sensors. The reference voltage isapplied by a reference electrode. The array of electronic sensorsincludes field effect transistors. The field effect transistors includeion sensitive field effect transistors.

In a related aspect, a solution flows through the sensor electrode. Aresponse of the sensor electrode is measured through the solution. Theresponse of the sensor electrode is amplified. An offset to the measuredresponse of the sensor electrode is provided to center the measuredresponse relative to a reference voltage. The response of the firstsubset of the array of electronic sensors is adjusted by scaling andsubtracting the response of the second subset of the array of electronicsensors.

According to various exemplary embodiments, there is provided a methodfor correcting nucleotide incorporation signals for fluid potentialeffects or disturbances arising in nucleic acid sequencing-by-synthesis,comprising: (a) disposing a plurality of template polynucleotide strandsin a plurality of defined spaces disposed on a sensor array, at leastsome of the template polynucleotide strands having a sequencing primerand a polymerase bound therewith; (b) exposing the templatepolynucleotide strands with the sequencing primer and a polymerase boundtherewith to a series of flows of nucleotide species flowed according toa predetermined ordering through a fluid manifold, the fluid manifoldcomprising passages for flowing nucleotide species and a branch passagefor flowing a solution not comprising nucleotide species, the branchpassage comprising a reference electrode and a sensing electrode; (c)obtaining a plurality of nucleotide incorporation signals correspondingto the plurality of defined spaces, the nucleotide incorporation signalshaving a signal intensity related to a number of nucleotideincorporations having occurred in the corresponding defined space; and(d) correcting at least some of the plurality of nucleotideincorporation signals for fluid potential effects or disturbances usinga mathematical transformation comprising a scale factor determined basedon signals obtained from the sensing electrode for each of a pluralityof regions of defined spaces on the sensor array.

According to various exemplary embodiments, there is provided anon-transitory machine-readable storage medium comprising instructionswhich, when executed and/or implemented by a processor, cause theprocessor to perform a method for correcting nucleotide incorporationsignals for fluid potential effects or disturbances arising in nucleicacid sequencing-by-synthesis comprising: (a) exposing a plurality oftemplate polynucleotide strands disposed in a plurality of definedspaces disposed on a sensor array and having a sequencing primer and apolymerase bound therewith to a series of flows of nucleotide speciesflowed according to a predetermined ordering through a fluid manifold,the fluid manifold comprising passages for flowing nucleotide speciesand a branch passage for flowing a solution not comprising nucleotidespecies, the branch passage comprising a reference electrode and asensing electrode; (b) obtaining a plurality of nucleotide incorporationsignals corresponding to the plurality of defined spaces, the nucleotideincorporation signals having a signal intensity related to a number ofnucleotide incorporations having occurred in the corresponding definedspace; and (c) correcting at least some of the plurality of nucleotideincorporation signals for fluid potential effects or disturbances usinga mathematical transformation comprising a scale factor determined basedon signals obtained from the sensing electrode for each of a pluralityof regions of defined spaces on the sensor array.

Additional objects and advantages of the disclosed embodiments will beset forth in part in the description that follows, and in part will beapparent from the description, or may be learned by practice of thedisclosed embodiments. The objects and advantages of the disclosedembodiments will be realized and attained by means of the elements andcombinations particularly pointed out in the appended claims.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory onlyand are not restrictive of the scope of disclosed embodiments, as setforth by the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated into and form a partof the specification, illustrate one or more exemplary embodiments andserve to explain the principles of various exemplary embodiments. Thedrawings are exemplary and explanatory only and are not to be construedas limiting or restrictive in any way.

FIG. 1 illustrates a schematic view of an example of an apparatus fordelivering reagents to reaction confinement areas, according toexemplary embodiments of the present disclosure;

FIG. 2 illustrates an electrical diagram of an example of a sensorarray, according to exemplary embodiments of the present disclosure;

FIG. 3 illustrates an electrical diagram of an example of an electronicsensor, according to exemplary embodiments of the present disclosure;

FIG. 4 illustrates an expanded and cross-sectional view of an exampleflow cell and a portion of an example flow chamber, according toexemplary embodiments of the present disclosure;

FIG. 5 illustrates an expanded view of an example well and an examplesensor, according to exemplary embodiments of the present disclosure;

FIG. 6 diagrammatically illustrates an example apparatus for carryingout pH-based nucleic acid sequencing, according to exemplary embodimentsof the present disclosure;

FIG. 7A illustrates an example of sensing electrode data, according toexemplary embodiments of the present disclosure;

FIG. 7B illustrates an example of electrical disturbance in reactionconfinement area data, according to exemplary embodiments of the presentdisclosure;

FIG. 8 illustrates an example of fluid potential signal correction,according to exemplary embodiments of the present disclosure;

FIG. 9A illustrates an example of simulated injection of noise insensing electrode signal, according to exemplary embodiments of thepresent disclosure;

FIG. 9B illustrates an example of simulated injection of noise in wellsignal, according to exemplary embodiments of the present disclosure;

FIGS. 10A and 10B illustrate examples of run statistics for a runincluding a relatively small amount of simulated noise, according toexemplary embodiments of the present disclosure;

FIGS. 11A and 11B illustrate examples of run statistics for a runincluding a relatively large amount of simulated noise, according toexemplary embodiments of the present disclosure;

FIGS. 12A and 12B illustrate run statistics and plots of error rates asa function of read position without correction for runs including arelatively large amount of simulated noise such as in FIGS. 11A and 11B,according to exemplary embodiments of the present disclosure;

FIGS. 13A and 13B illustrate run statistics and plots of error rates asa function of read position with correction for runs including arelatively large amount of simulated noise such as in FIGS. 11A and 11B,according to exemplary embodiments of the present disclosure;

FIGS. 14A and 14B illustrate error rates and coverage depth for runswithout (FIG. 14A) and with (FIG. 14B) fluid potential artifactcorrection, according to exemplary embodiments of the presentdisclosure;

FIGS. 15A and 15B illustrate examples of simultaneous measurementsshowing different response across columns for a non-common mode noise,according to exemplary embodiments of the present disclosure;

FIGS. 16A and 16B illustrate examples of a spatial distribution of errorrates for a non-common mode noise after a flow resulting in significanterrors, according to exemplary embodiments of the present disclosure;

FIGS. 17A and 17B illustrate examples of a spatial distribution of errorrates for a non-common mode noise after a flow not resulting insignificant errors, according to exemplary embodiments of the presentdisclosure; and

FIG. 18 illustrates an exemplary computer system, according to exemplaryembodiments of the present disclosure.

DETAILED DESCRIPTION OF EMBODIMENTS

The following description and the various embodiments described hereinare exemplary and explanatory only and are not to be construed aslimiting or restrictive in any way. Other embodiments, features,objects, and advantages of the present teachings will be apparent fromthe description and accompanying drawings, and from the claims.

In this application, “defined space” generally refers to any space(which may be in one, two, or three dimensions) in which at least someof a molecule, fluid, and/or solid can be confined, retained and/orlocalized. The space may be a predetermined area (which may be a flatarea) or volume, and may be defined, for example, by a depression or amicro-machined well in or associated with a microwell plate, microtiterplate, microplate, or a chip, or by isolated hydrophobic areas on agenerally hydrophobic surface. Defined spaces may be arranged as anarray, which may be a substantially planar one-dimensional ortwo-dimensional arrangement of elements such as sensors or wells.Defined spaces, whether arranged as an array or in some otherconfiguration, may be in electrical communication with at least onesensor to allow detection or measurement of one or more detectable ormeasurable parameters or characteristics. The sensors may convertchanges in the presence, concentration, or amounts of reactionbyproducts (or changes in ionic character of reactants) into an outputsignal, which may be registered electronically, for example, as a changein a voltage level or a current level which, in turn, may be processedto extract information or signal about a chemical reaction or desiredassociation event, for example, a nucleotide incorporation event and/ora related ion concentration (e.g., a pH measurement). The sensors mayinclude at least one ion sensitive field effect transistor (“ISFET”) orchemically sensitive field effect transistor (“chemFET”). Defined spacesmay sometimes be referred to as reaction confinement areas, which may inan example represent microwells in a semiconductor chip.

FIG. 1 illustrates a schematic view of an example of an apparatus fordelivering reagents to reaction confinement areas. The apparatus 100 mayinclude a solution reservoir 146, which may include a solution 142(which may be a wash solution); a plurality of reagent reservoirs 144,which may include a plurality of corresponding reagents 140; a fluidmanifold 150, which may be in fluidic communication with the solutionreservoir 146 and the plurality of reagent reservoirs 144; a branchpassage 190, which may be in fluidic communication with the fluidmanifold 150; an outlet passage 160, which may be in fluidiccommunication with the branch passage 190 and the fluid manifold 150;and a flow cell 110, which may be in fluidic communication with theoutlet passage 160 and may be a semiconductor chip. The fluid manifold150 may include a reference electrode 170, which may provide a referencevoltage 172, and a sensor electrode 180 (provided downstream of thereference electrode 170, that is, closer to the outlet passage 160 thanthe reference electrode 170), which may be coupled to an amplifier 182providing a reference voltage offset 184 to an output of the sensorelectrode 180. The reference electrode 170 and the sensor electrode 180may contact fluid (such as the solution 142) flowing within the branchpassage 190, and reference electrode 170 and sensor electrode 180 may befree of direct contact with any of the reagents 140 that may be flowingthrough the outlet passage 160.

The flow cell 110 may include a plurality of reaction confinement areas120 cooperatively engaged with a first array of electronic sensors 130in fluidic communication with the fluid in the reaction confinementareas 120. As discussed in detail below with regard to FIG. 2, eachreaction confinement area 120 has a corresponding electronic sensor 130.The flow cell 110 may also include a second array of electronic sensors132 not in fluidic communication with the fluid in the reactionconfinement areas 120.

The first and second arrays of electronic sensors 130 and 132 may befield-effect transistors having gate electrodes, which may includeISFETs or chemFETs. Each electronic sensor 132 of the second array ofelectronic sensors 132 may include a gate electrode 134 in electricalcommunication with the sensor electrode 180. In an example, theamplifier 182 may be in electrical communication between the output ofthe sensor electrode 180 and the gate electrode 134 of field-effecttransistors of the second array of electronic sensors 132.

As shown in FIG. 1, the flow cell 110 may include a fluid inlet 162 influidic communication with the outlet passage 160, and a fluid outlet164 in fluidic communication with the flow cell 110. The sensorelectrode 180 may be in electrical communication with the first array ofelectronic sensors 130 through fluid via the fluid inlet 162 or thefluid outlet 164. As will be discussed below with FIG. 2, the first andsecond arrays of electronic sensors 130 and 132 may be arranged in rowsand columns such that the second array of electronic sensors 132includes a column of electronic sensors, and each sensor in the columnmay be in electrical communication with the output of the sensorelectrode 180 through a solution via the outlet passage 160.

FIG. 2 illustrates an electrical diagram of an example of a sensorarray. The sensor array 200 may include a plurality of electronicsensors 210 and 220. A first subset 240 of electronic sensors mayinclude the plurality of electronic sensors 210 (see, for example, thesecond and third column from the left of FIG. 2), which may be exposedto one or more fluids (such as a wash solution or reagents) via fluidaccess to corresponding reaction confinement areas 240 a. A secondsubset 250 of electronic sensors may include the plurality of electronicsensors 220 (see, for example, the first column from the left of FIG.2), which may be free of contact with any fluid within the reactionconfinement areas 240 a.

In an embodiment of the present disclosure, each electronic sensor 210may include a corresponding reaction confinement area 240 a (alsoreferred to as a well 240 a), and a field-effect transistor, which mayinclude ISFETS having a gate electrode 242. The reaction confinementareas 240 a of FIG. 2 may correspond to the reaction confinement areas120 of FIG. 1, and the electronic sensors 210 of FIG. 2 may correspondto the electronic sensors 130 of FIG. 1.

Each electronic sensor 220 may include a corresponding field-effecttransistor, which may include ISFETS having a gate electrode 222. Theelectronic sensors 220 of FIG. 2 may correspond to the electronicsensors 132 of FIG. 1. Further, the gate electrode 134 of field-effecttransistors of the second array of electronic sensors 132 of FIG. 1 maycorrespond to the gate electrode 222 of field-effect transistors of theelectronic sensors 220.

A sensor electrode 260 may be in electrical communication with the firstsubset 240 of electronic sensors through fluid in the reactionconfinement areas 240 a. A sensor electrode output 262 may be inelectrical communication with the gate electrodes 222 of the secondsubset 250 of electronic sensors. The sensor electrode 260 of FIG. 2 maycorrespond the sensor electrode 180 of FIG. 1.

As shown in FIG. 2, the sensor array 200 may be arranged in rows andcolumns such that the second subset 250 of sensors includes a column ofelectronic sensors 220, which may be in electrical communication withthe sensor electrode output 262. The sensor electrode output 262 may besampled and measured by the second subset 250 of sensors in the samemanner the reaction confinement area 240 a signals may be sampled andmeasured by the first subset 240 of sensors.

A row select switch (not shown) may be connected to one through N rowselect switch lines 212 (see, for example, ROWSEL 1, ROWSEL 2, . . . ,ROWSEL N of FIG. 2), where N is a number of rows of electronic sensorsof sensory array 200. The row select switch may be used to select one ormore rows of electronic sensors 210 and 220 of the sensor array 200. Theselecting of one or more rows of electronic sensors 210 and 220 of thesensory array 200, however, may lead to an undesirable coupling ofsignals into fluid via capacitance of column metallization.

In an embodiment, the measured response from of an electronic sensor 220of the second subset 250 in a row with a plurality of electronic sensors210 of the first subset 240 may be used to adjust the measured responseof the electronic sensors 210 within the same row. For example, theresponse of the first subset 240 of electronic sensors 210 may beadjusted by scaling and subtracting the response of the correspondingsecond subset 250 of electronic sensors 220 for each selected row.

FIG. 3 illustrates an electrical diagram of an example of an electronicsensor 300. Shown are various resistances and/or capacitances that mayintroduce error into measurements of the electronic sensor 300. Areference electrode 310 (which may correspond to the reference electrode170 of FIG. 1) may provide a bias voltage 312 (which may correspond toreference voltage 172 of FIG. 1) for a sensor array, such as sensorarray 200 of FIG. 2.

A sensor electrode 320 (which may correspond to sensor electrode 180 ofFIG. 1) may output a measured response to an amplifier 324 (which maycorrespond to amplifier 182 of FIG. 1). A reference voltage offset 326may be provided to the amplifier 324 and may be an offset to themeasured response of the sensor electrode 320 to center the measuredresponse relative to the reference voltage 312. The amplifier output 328may then be provided to unused, non-well electronic sensors (such as,e.g., the second subset 250 of electronic sensors 220, which are not incontact with fluid described in FIG. 2).

Sources of error, as depicted in FIG. 3, may include: fluid resistance330, leakage resistance 340, overall metallization stray column-to-fluidcoupling capacitance 350, row-switch voltage transient 352, overall wellresistance 360, overall well capacitance 362, per-well resistance 364,and per-well capacitance 366. In addition, an electrostatic discharge(“ESD”), which may result from touching of fluid tubes, human contact,etc., may undesirably couple into the fluid and cause measurementdisruption. While FIG. 3 depicts example resistances and/orcapacitances, these resistances and/or capacitances are not limited tosuch depicted values.

Measurement Operation

Exemplary operation of an apparatus and sensory array, as illustrated inFIGS. 1 and 2, will now be described in detail.

In an embodiment, a reagent 140, such as from one of the reagentreservoirs 144 of the plurality of reagent reservoirs 144, may flow viathe fluid manifold 150 into a flow cell 110 having a sensory array, suchas sensor array 200 of FIG. 2. The reagent 140 may react to provide areaction product within one or more of the plurality of reactionconfinement areas 120 of FIG. 1 or the one or more of the plurality ofreaction confinement areas 240 a of FIG. 2.

A solution 142, such as from the solution reservoir 14, may also flowvia the fluid manifold 150 and branch passage 190 (which may include thereference electrode 170 and the sensor electrode 180 of FIG. 1). Thereference electrode 170 may apply the reference voltage 172 through thesolution 142, which is in fluidic communication with the flow cell 110having the sensory array, such as sensor array 200 of FIG. 2, and withthe first array of electronic sensors 130 (the plurality of electronicsensors 210 of the first subset 240 of FIG. 2). A response (e.g.,voltage) of the sensor electrode 180 (sensor electrode 260 of FIG. 2)may be measured through the solution 142 and may be amplified by theamplifier 182 providing the reference voltage offset 184.

In the flow cell 110 having the sensor array, such as sensor array 200,a first array of electronic sensors 130 (the plurality of electronicsensors 210 of the first subset 240 of FIG. 2) may measure a response(e.g., voltage) to the reaction product, and a second array ofelectronic sensors 132 (the plurality of electronic sensors 220 of thesecond subset 250 of FIG. 2), which may be in electrical communicationwith the sensor electrode 180 (sensor electrode 260 of FIG. 2) but maynot be in fluid communication with the plurality of reaction confinementareas 120 (reaction confinement areas 240 a of FIG. 2). An output of theamplifier 182 may be provided as an input to the second array ofelectronic sensors 132 (i.e., to the sensor electrode output 262connected to the plurality of electronic sensors 220 of the secondsubset 250). The output of the amplifier 182 may be used to center themeasured response relative to the reference voltage 172. The response ofthe first array of electronic sensors 130 (the electronic sensors 210 ofFIG. 2) may be adjusted by scaling and subtracting the response of thesecond array of electronic sensors 132 (the electronic sensors 220 ofFIG. 2).

As discussed above, the first array of electronic sensors 130 (the firstsubset 240 of electronic sensors 210 of FIG. 2) and the second array ofelectronic sensors 132 (the second subset 250 of electronic sensors 220of FIG. 2) may represent an array of electronic sensors arranged in rowsand columns. For example, the first array of electronic sensors 130 mayinclude a first subset 240 of electronic sensors 210 (see, for example,the second and third column from the left of FIG. 2) exposed to thereagent solution 140 within the a flow cell 110 having a sensor array,such as the sensor array 200. The second array of electronic sensors 132may include a second subset 250 of electronic sensors 220 (see, forexample, the first column from the left of FIG. 2).

The output of the sensor electrode 180 (sensor electrode 260 of FIG. 2)may be in electrical communication with each electronic sensor 132 (eachelectronic sensor 220 of FIG. 2 within the column of electronic sensors220 of the second subset 250. The second subset 250 of electronicsensors 220 may be free of contact with the reagent solution fluid 140within the flow cell 120 having the sensor array (sensor array 200) andmay instead be in electrical contact with the output of thesensor-electrode amplifier (182) output 260.

In an example embodiment, a sequencing system may include a flow cellhaving a sensory array, communication circuitry in electroniccommunication with the sensory array, and containers and fluid controlsin fluidic communication with the flow cell. FIG. 4 illustrates anexpanded and cross-sectional view of a flow cell 400 and illustrates aportion of a flow chamber 406. A reagent 408, such as a reagent 140 fromone of the plurality of reagent reservoirs 144, may flow across asurface 402 a of a well array 402. For example, the reagent 408 may flowover the open ends of a plurality of wells of the well array 402. Asensor array 405 may be disposed adjacent to the well array 402, and thesensory array 405 and the well array 402 may together form an integratedunit forming a lower wall (or floor) of the flow cell 400. A referenceelectrode 404 may be fluidically coupled to flow chamber 406. Further, aflow cell cover 412 may encapsulate flow chamber 406 to contain reagent408 within a confined region.

FIG. 5 illustrates an expanded view of a well 510 and a sensor 514, suchas a well of the well array 402 and a sensor of the sensor array 405, asillustrated at 410 of FIG. 4. The volume, shape, aspect ratio (such asbase width-to-well depth ratio), and other dimensional characteristicsof the wells may be selected based on the nature of the reaction takingplace, as well as the reagents, byproducts, or labeling techniques (ifany) that may be employed.

The sensor 514 of the sensor array may be a field-effect transistor(“FET”), such as a chemFET, or, for example, more specifically an ISFET.The field-effect transistor may have a floating gate 518 including asensor plate 520. The floating gate 518 of the field-effect transistorymay optionally separated from an interior area of the well 510 by amaterial layer 516. In addition, a conductive layer (not illustrated)may be disposed over the sensor plate 520. In an example, the materiallayer 516 may include an ion sensitive material layer. The materiallayer 516 may be a ceramic layer, such as an oxide of zirconium,hathium, tantalum, aluminum, or titanium, among others, or a nitride oftitanium. Alternatively, the material layer 516 may be formed of ametal, such as titanium, tungsten, gold, silver, platinum, aluminum,copper, or a combination thereof. In an example, the material layer 516may have a thickness in a range of 5 nm to 100 nm+/−15%, such as a rangeof 10 nm to 70 nm, a range of 15 nm to 65 nm, or even a range of 20 nmto 50 nm.

While the material layer 516 is illustrated as extending beyond thebounds of the illustrated FET component, the material layer 516 mayextend along the bottom of the well 510, and the material layer 516 mayoptionally extend along the walls of the well 510. The sensor 514 may beresponsive to (and may generate an output signal related to) the amountof a charge 524 present on the well 510 side of the material layer 516that opposes the sensor plate 520 side of the sensor 514.

Changes in the charge 524 may cause changes in a current between asource 521 and a drain 522 of the FET. In turn, the FET of the sensor514 may be used directly to provide a current-based output signal and/orindirectly with additional circuitry to provide a voltage-based outputsignal. Reactants, wash solutions, and other reagents may move in andout of the well 510 by a diffusion mechanism 540.

In one embodiment, reactions carried out in the well 510 may beanalytical reactions to identify or determine characteristics orproperties of an analyte of interest. Such reactions may generatedirectly or indirectly byproducts that affect the amount of chargeadjacent to the sensor plate 520. If such byproducts are produced insmall amounts, rapidly decay, and/or react with other constituents,multiple copies of the same analyte may be analyzed in the well 510 atthe same time in order to increase the output signal generated.

In an embodiment of the present disclosure, multiple copies of ananalyte may be attached to a solid phase support 512, either before orafter deposition into the well 510. The solid phase support 512 may be apolymer matrix, such as a hydrophilic polymer matrix, for example, ahydrogel matrix or the like. For simplicity and ease of explanation, thesolid phase support 512 may also be referred herein as a polymer matrix.

The well 510 may be defined by a wall structure, which may be formed ofone or more layers of material. In one embodiment, the wall structuremay have a thickness extending from the lower surface to the uppersurface of the well in a range of 0.01 micrometers to 10micrometers+/−15%, such as a range of 0.05 micrometers to 10micrometers, a range of 0.1 micrometers to 10 micrometers, a range of0.3 micrometers to 10 micrometers, and/or a range of 0.5 micrometers to6 micrometers. In a particular embodiment, the thickness may be in arange of 0.01 micrometers to 1 micrometer+/−15%, such as a range of 0.05micrometers to 0.5 micrometers, or a range of 0.05 micrometers to 0.3micrometers. The well 510 may have a characteristic diameter, defined asthe square root of 4 times the cross-sectional area (A) divided by Pi(e.g., sqrt(4*A/π), of not greater than 5 micrometers, such as notgreater than 3.5 micrometers, not greater than 2.0 micrometers, notgreater than 1.6 micrometers, not greater than 1.0 micrometers, notgreater than 0.8 micrometers or even not greater than 0.6 micrometers.In an example embodiment, the well 510 may have a characteristicdiameter of at least 0.01 micrometers+/−15%. In a further exampleembodiment, the well 510 may define a volume in a range of 0.05 fL to 10pL+/−15%, such as a volume in a range of 0.05 fL to 1 pL, a range of0.05 fL to 100 fL, a range of 0.05 fL to 10 fL, or even a range of 0.1fL to 5 fL.

While FIG. 5 illustrates a single-layer wall structure and asingle-layer material layer 516, the system may include one or more wallstructure layers, one or more conductive layers, and/or one or morematerial layers. For example, the wall structure may be formed of one ormore layers, including an oxide of silicon, tetraethyl orthosilicate(“TEOS”), and/or a nitride of silicon.

Nucleic acid beads may be loaded into a biosensor for determiningcharacteristics of the nucleic acid beads. In particular, the nucleicacid beads may be used for sequence target sequences conjugated to thenucleic acid beads. For example, sequencing may include label-free DNAsequencing, and in particular, pH-based DNA sequencing. Substratesincluding DNA templates and having a primer and polymerase operablybound may be loaded into reaction confinement areas (such as reactionconfinement areas 120 of FIG. 1, reaction confinement areas 240 a ofFIG. 2, and/or a well 510 of FIG. 5), after which repeated cycles ofdeoxynucleoside triphosphate (“dNTP”) addition and washing may becarried out. Such templates may be attached as clonal populations to thesubstrate, such as a microparticle, bead, or the like, and such clonalpopulations may be loaded into reaction confinement areas. In eachadditional step of the cycle, the polymerase may extend the primer byincorporating added dNTP when the next base in the template is thecomplement of the added dNTP.

When there is one complementary base, there may be one incorporation,when two, there may be two incorporations, when three, there may bethree incorporations, and so on. With each such incorporation there maybe a hydrogen ion released, and collectively a population of templatesreleasing hydrogen ions may cause very slight changes in the local pH ofthe reaction confinement area, which may be detected by an electronicsensor (such as sensor 514 of FIG. 5).

FIG. 6 diagrammatically illustrates an apparatus for carrying outpH-based nucleic acid sequencing. Each electronic sensor of theapparatus may generate an output signal that depends on the value of areference voltage. In FIG. 6, a housing 600 may contain fluidics circuit602 that may be connected by inlets to reagent reservoirs 604, 606, 608,610, and 612 (such as the plurality of reservoirs 144 of FIG. 1), towaste reservoir 620, and to flow cell 634 (such as flow cell 110 ofFIG. 1) by passage 632 that may connect fluidics node 630 to inlet 638of flow cell 634. Reagents from reservoirs 604, 606, 608, 610, and 612may be driven to fluidic circuit 602 by a variety of methods including,but not limited to, pressure, pumps, such as syringe pumps, gravityfeed, and the like, and may be selected by control of valves 614.Control system 618 may include controllers for valves 614 that generatesignals for opening and closing via an electrical connection 616.Control system 618 may also include controllers for other components ofthe system, such as wash solution valve 624 connected thereto by anelectrical connection 622, and reference electrode 628 by an electricalconnection.

Control system 618 may also include control and data acquisitionfunctions for flow cell 634. In one mode of operation, fluidics circuit602 may deliver a sequence of selected reagents (such as reagents 1, 2,3, 4, and 5) to flow cell 634 under programmed control of control system618, such that in between selected reagent flows, fluidics circuit 602may be primed and washed, and flow cell 634 may washed. Fluids enteringflow cell 634 may exit through an outlet 640 and may be deposited in awaste container 636. Throughout such an operation, the reactions ormeasurements taking place in flow cell 634 may have a stable referencevoltage because reference electrode 628 has a continuous, i.e.uninterrupted, electrolyte pathway with flow cell 634, but is inphysical contact with the wash solution 626.

An exemplary apparatus may include a device including a flow cell influid communication with an electronic sensor, a plurality of reagentreservoirs to include a plurality of reagents, a fluid manifold influidic communication with the plurality of reagent reservoirs, anoutlet passage of the fluid manifold in fluid communication with theflow cell, a reference electrode to provide a reference voltage to theelectronic sensor through fluid in the outlet passage and the flow cell,and a sensor electrode in electrical communication with the fluid of theoutlet passage and the flow cell. The fluid manifold may further includea branch passage between the fluid manifold and the flow cell in fluidcommunication with the outlet passage. The reference electrode may bedisposed in contact with fluid within the branch passage. The referenceelectrode may be free of direct contact with any reagent of theplurality of reagents when the any reagent flows through the outletpassage. The sensor electrode may be disposed in contact with the fluidwithin the branch passage. The sensor electrode may be disposed closerto the outlet passage than the reference electrode. The sensor electrodemay be free of direct contact with any reagent of the plurality ofreagents when the any reagent flows through the outlet passage. Theapparatus may further include a solution reservoir in fluidcommunication with the branch passage. The apparatus as in any one ofthe preceding examples may further include a second electronic sensornot in fluid communication with the flow cell, the second electronicsensor including a gate electrode, and an output from the sensorelectrode in electrical communication with the gate electrode. Theapparatus as in any one of the preceding examples may further include anamplifier coupled to the sensor electrode and providing a referencevoltage offset to the sensor electrode. The apparatus as in any one ofthe preceding examples may further include an electronic sensorincluding a field effect transistor including a gate electrode. Theapparatus as in any one of the preceding examples may further include anelectronic sensor including an ion sensitive field effect transistor.

Another exemplary apparatus may include a flow cell including a fluidinlet and a fluid outlet, an array of electronic sensors cooperativelyengaged with the flow cell, each of the electronic sensors including afield effect transistor including a gate electrode, a first subset ofthe array of electronic sensors exposed to a fluid within the flow cell,a second subset of the array of electronic sensors free of contact withthe fluid within the flow cell, and a sensor electrode in electricalcommunication with the first subset of the array of electronic sensorsthrough fluid via the fluid inlet or the fluid outlet, an output of thesensor electrode in electrical communication with the gate electrodes ofthe field effect transistors of the second subset of the array ofelectronic sensors. The array of electronic sensors may be arranged inrows and columns, wherein the second subset of the array of electronicsensors includes a column of electronic sensors, the output of thesensor electrode in electrical communication with the each electronicsensor within the column of electronic sensors of the second subset ofthe array of electronic sensors. The apparatus may further include afluid manifold in fluid communication with a plurality of reagentreservoirs, the fluid manifold including an outlet passage in fluidcommunication with the fluid inlet, the sensor electrode in electricalcommunication with the second subset of the array of electronic sensorsthrough a solution via the outlet passage. The apparatus may furtherinclude a branch passage between the fluid manifold and the flow cell influid communication with the outlet passage, the sensor electrodedisposed in the branch passage. The reference electrode may be disposedin contact with fluid within the branch passage. The reference electrodemay be free of direct contact with any reagent of the plurality ofreagents when the any reagent flows through the outlet passage. Thesensor electrode may be disposed in contact with fluid within the branchpassage. The sensor electrode may be disposed closer to the outletpassage than the reference electrode. The sensor electrode may be freeof direct contact with any reagent of the plurality of reagents when theany reagent flows through the outlet passage. The apparatus may furtherinclude a solution reservoir in fluid communication with the branchpassage. The plurality of reagent reservoirs may include a plurality ofreagents. The apparatus as in any one of the preceding examples mayfurther include a reference electrode to provide a reference voltage tothe first subset of the array of electronic sensors through a solutionvia the fluid inlet or the fluid outlet. The apparatus as in any one ofthe preceding examples may further include an array of wells providingfluid access to the gate electrodes of the field effect transistors ofthe first subset of the array of electronic sensors. The apparatus as inany one of the preceding examples may further include an amplifierdisposed in electrical communication between the output of the sensorelectrode and the gate electrodes of the field effect transistors of thesecond subset of the array of electronic sensors. The apparatus as inany one of the preceding examples may further include the field effecttransistors of the first subset of the array of electronic sensorsincluding ion sensitive field effect transistors.

An exemplary method of measuring a reaction product includes flowing areagent solution into a flow cell, the reagent solution reacting toprovide a reaction product, the flow cell in fluid communication with afirst electronic sensor, measuring a response of the first electronicsensor to the reaction product, measuring a response of a secondelectronic sensor, the second electronic sensor in electricalcommunication with a sensor electrode in fluid communication with theflow cell, the second electronic sensor not in fluid communication withthe flow cell, and adjusting the response of the first electronic sensorbased on the response of the second electronic sensor. The method mayfurther include applying a reference voltage through a solution in fluidcommunication with the flow cell in fluid communication with the firstelectronic sensor. The reference voltage is applied by a referenceelectrode. The first electronic sensor and the second electronic sensorinclude field effect transistors. The field effect transistor of thefirst electronic sensor may include an ion sensitive field effecttransistor. The method may further include flowing a solution throughthe sensor electrode, measuring a response of the sensor electrodethrough the solution, and amplifying the response of the sensorelectrode. The method may further include providing an offset to themeasured response of the sensor electrode to center the measuredresponse relative to a reference voltage. The method as in any one ofthe preceding examples may include the response of the first electronicsensor being adjusted by scaling and subtracting the response of thesecond electronic sensor.

Another exemplary method of measuring a reaction product includesflowing a reagent solution into a flow cell, the reagent solutionreacting to provide a reaction product, the flow cell in fluidcommunication with an array of electronic sensors cooperatively engagedwith the flow cell, a first subset of the array of electronic sensorsexposed to the reagent solution within the flow cell, a second subset ofthe array of electronic sensors free of contact with the reagentsolution fluid within the flow cell, measuring a response of the firstsubset of the array of electronic sensors to the reaction product,measuring a response of the second subset of the array of electronicsensors, the second subset of the array of electronic sensors inelectrical communication with a sensor electrode in fluid communicationwith the flow cell, and adjusting the response of the first subset ofthe array of electronic sensors based on the response of the secondsubset of the array of electronic sensors. The method may include eachof the electronic sensors including a field effect transistor includinga gate electrode, and the sensor electrode in electrical communicationwith the first subset of the array of electronic sensors through fluid,an output of the sensor electrode in electrical communication with thegate electrodes of the field effect transistors of the second subset ofthe array of electronic sensors. The method may include the array ofelectronic sensors being arranged in rows and columns, wherein thesecond subset of the array of electronic sensors includes a column ofelectronic sensors, the output of the sensor electrode in electricalcommunication with the each electronic sensor within the column ofelectronic sensors of the second subset of the array of electronicsensors. The method may further include applying a reference voltagethrough a solution in fluid communication with the flow cell in fluidcommunication with the first subset of the array of electronic sensors.The method may include the reference voltage being applied by areference electrode. The method may include the array of electronicsensors including field effect transistors. The method may include fieldeffect transistors including ion sensitive field effect transistors. Themethod as in any one of the preceding examples may further includeflowing a solution through the sensor electrode, measuring a response ofthe sensor electrode through the solution, and amplifying the responseof the sensor electrode. The method as in any one of the precedingexamples may further include providing an offset to the measuredresponse of the sensor electrode to center the measured responserelative to a reference voltage. The method as in any one of thepreceding examples may include the response of the first subset of thearray of electronic sensors being adjusted by scaling and subtractingthe response of the second subset of the array of electronic sensors.

Sensing Electrode Data

FIG. 7A illustrates an example of sensing electrode data. In thisexample, a sensing electrode signal may be sampled at a rate of 30 Hzfor each of 100 rows in a region of 100×100 wells in a sample array. Thex-axis represents time during sensing, expressed in seconds. The y-axisrepresents voltage, expressed in counts (which may be for practicalpurposes proportional to voltage, with 1 count representing 2.5 mV). Thesensing electrode signal may be measured in the same way as wellsignals, and the amplified signal from the sensing electrode may beapplied to unused ISFET transistor columns. The sense electrode and wellreadings may be simultaneous for the same row. As shown in FIG. 7A, thetraces for the various rows may be similar, and there may appear to be arelatively clear three-peak electrical disturbance 700 a in fluidpotential shortly before the three-second mark.

FIG. 7B illustrates an example of electrical disturbance in reactionconfinement area data. In this example, a reaction confinement areasignal may be sampled at a rate of 30 Hz for each well in a region of100×100 wells comprising ISFETs in contact with fluid in a sample array.The x-axis represents time during sensing, expressed in seconds. They-axis represents voltage, expressed in counts (which may be forpractical purposes proportional to voltage). As shown in FIG. 7B, thetraces for the various wells may be similar, and the three-peakelectrical disturbance 700 a in fluid potential picked-up relativelyclearly in the sensing electrode data of FIG. 7A may appear to also bepresent in the data of FIG. 7B, as three-peak electrical disturbance 700b (albeit less clearly given that the disturbance occurred at a timewhere the level of counts was much higher than the baseline of aroundzero or so in FIG. 7A).

In one embodiment, sensing electrode signals acquired simultaneouslywith the well signal may be used to remove some or all high frequencynoise using an appropriate mathematical transformation. In an example,the mathematical transformation may use an expressionw_(c)(t)=w(t)−αs(t), where w_(c)(t) represents a corrected well signal,w(t) represents an initial or uncorrected well signal, s(t) represents asensing electrode signal, and α represents a scale factor. The scalefactor α may be determined or estimated in any suitable way, which maybe analytical, model-based, and/or empirical or some combinationthereof.

In an example, the scale factor α may be determined as follows: (1) fora fixed α, calculate w_(c)(t) using the above formula for each well in aregion of wells (e.g., 100 by 100 wells); (2) calculate the averagetrace w_(c) (t) to remove non-common-mode noise; (3) fit w_(c) (t) withlocal polynomials; (4) calculate a mean square error of w_(c) (t) fromthe fit; and (5) select the optimal scale factor α that minimizes themean square error. In the above steps, any suitable means for selectingfixed starting point estimates, calculating average traces, fittingfunctions to polynomials, and calculating mean square errors may beused. Regarding step (1) in particular, any suitable means for selectingfixed starting point estimates may be used, however, preferably a listof values of a may be predetermined from 0 to 10 at 0.2 intervals.Regarding step (3) in particular, any suitable local polynomial may beused, however, preferably the local polynomials may be determined usinga digital filter that may be applied to a set of digital data points forthe purpose of smoothing the data, that is, to increase thesignal-to-noise ratio without greatly distorting the signal. Such adigital filter may be a Savitzky-Golay filter, for example, and furtherpreferably using a 2^(nd) order Savitzky-Golay filter and 7 frames. Thefollowing document relates to digital filters, such as a Savitzky-Golayfilter, and is incorporated by reference herein in its entirety:Savitzky & Golay, “Smoothing and Differentiation of Data by SimplifiedLeast Squares Procedures,” Analytical Chemistry, 36(8):1627-39 (1964).

In various embodiments, other filters likely to maintain meaningfultransients (e.g., a pH step) while removing most of the high frequencynoise (e.g., a median filter, a finite impulse response (“FIR”) low passfilter, a FIR Filter, an infinite impulse response (“IIR”) low passfilter, an IIR filter, etc.) may be used although such other filters mayor may not work as well as a Savitzky-Golay filter.

In an embodiment, a scale factor α determined as described above may befurther determined using an additional step as follows: (6) refine theselected optimal scale factor α by applying a quadratic fit to the scalefactor α that minimizes the error and its nearest neighbors. Forexample, if α=5.2 minimizes mean square error with value err(5.2), αvalues x=5.0, 5.2, and 5.4 and y=err(5.0), err(5.2), and err(5.4) may beused to fit with quadratic equation y=a x²+b x+c. The re-estimatedoptimal scale factor α may then be given by the minimum as predicted bythe quadratic equation, i.e., −b/2a. The advantage of this additionalstep may be to remove a quantization artifact introduced by thearbitrary interval size of 0.2, while allowing relatively large stepsize (e.g., 0.2) to improve performance.

In an embodiment, sensing electrode signals acquired simultaneously withthe well signal may be used to remove some or all high frequency noiseusing an appropriate mathematical transformation implemented using amethod, system, and/or computer-readable medium, which may includeinstructions as set forth in the following samples of code, which areexemplary only and not limiting in any way.

An example of source code for removal of some or all high frequencynoise using a transformation is provided below:

/* RowSumData.h */ #ifndef ROWSUMDATA_H_(—) #define ROWSUMDATA_H_(—)#include <fstream> #include<vector> #include “../datahdr.h” #include<algorithm> class RowSumData { public:   RowSumData( );   virtual~RowSumData( );   // read rowsum data from file store raw data in rowsumprivate member   // return 0 if success; return 1 if error opening file;return 2 if error reading or   // closing file   intLoadRowSumData(const std::string fileName, const std::vector<unsignedint> startRowList, const std::vector<unsigned int> endRowList);   //return the sensing electrode trace in full resolution  std::vector<float> RowTrace(const unsigned int row);   // return the4-row averaged sensing electrode trace in full resolution  std::vector<float> RowTrace_avg4(const unsigned int row);   // returnthe 4-row averaged sensing electrode trace in full resolution with trace  // offset adjusted to zero by subtracting the average of the firstnumOffsetFrames   // points   std::vector<float> RowTrace_avg4(constunsigned int row, const unsigned int numOffsetFrames);   // return the4-row averaged sensing electrode trace in time compressed   //resolution with trace offset adjusted to zero by subtracting the averageof the   // first numOffsetFrames points the frames are compressedaccording to the new // time stamps, normalized by the rowsum frameinterval   std::vector<float> RowTrace_avg4(const unsigned int row,const unsigned int numOffsetFrames, const std::vector<unsigned int>newTimeStamps);   // return total number of rows   unsigned int NumRows();   // return frame rate in msec   float FrameRate( );   // return timestamp   // normalized = true: returns time stamps normalized by frameintervals   // normalized = false: returns time stamps in msec  std::vector<unsigned int> TimeStamps(bool normalized);   unsigned intRow2avg4row(const unsigned int wholeChipRow);   // convert row in wholechip coordinate to the corresponding row in   // senseTrace_avg4   voidRow2RowsumRows(const unsigned int row, std::vector<unsigned int> &rowsumRows);   std::vector<float> CompressFrames(conststd::vector<float> & rowTrace, std::vector<float> & rowTrace_vfc, conststd::vector<unsigned int> & timeStampOrig, const std::vector<unsignedint> & timeStampNew);   // return if the 4-row-averaged sensingelectrode trace is valid row is whole chip   // row   boolisValidAvg4(unsigned int row); private:   // compute sensing electrodetraces in (row,frame) format   void ComputeSenseTrace( );   // filterthe trace with median filter   void medianFilterTrace(const unsigned intorder);   // calculate median   float median(const float * v1, constunsigned int order);   // compute sense electrode traces, averaged overfour rows that are acquired   // simultaneously   voidComputeSenseTrace_avg4( );   // adjust the offset of trace to zero byzeroing the first numOffsetFrames frames   voidZeroTrace(std::vector<float> & trace, const unsigned intnumOffsetFrames);   std::vector<uint32_t> rowsum;   // row sum raw datafrom file   std::vector<std::vector<float> > senseTrace;   // rowsumdata averaged by pixelsInSum (only the needed rows are populated)  std::vector<std::vector<float> > senseTrace_avg4;   // 4 row averagedsensing electrode data   std::vector< bool > isValid_avg4;   // whetherthe 4-row-averaged sensing electrode data is valid   floatbaseFrameRate; // in msec defined the same rate as in raw struct (floatas // int does not have enough precision when calculating frame numbers)  uint32_t pixelsInSum; // number of pixels summed in each rowsum data  uint32_t sumsPerRow; // number of rowsum values per row   uint32_tsskey; // the first field in the header of a rowsum file   uint32_tversion; // version number of rowsum data file   uint32_t numRows; //total number of rows of the chip   uint32_t numFrames; // number offrames in the rowsum data   std::vector<unsigned int> startRowList;   //first row of ISFET and/or chemFET data in whole chip coordinate  std::vector<unsigned int> endRowList;   // last + 1 row of ISFETand/or chemFET data in whole chip coordinate   std::string fileName; //file name of the rowsum file   std::vector<bool> isValid; // whether arowsum trace is valid   std::vector<bool> isNeeded; // whether a row isneeded from the data (if   // isNeeded rows will go through furtherprocessing)   uint32_t lowPin, highPin;   // low and high values forpinned rowsum   unsigned int numPinnedLow, numPinnedHigh;   // number oflow and high pin values in the rows needed   bool DEBUG;   booltopHalfOnly; }; #endif /* ROWSUMDATA_H_ */

Further exemplary source code for removal of some or all high frequencynoise using a transformation is provided below:

Further exemplary source code for removal of some or all high frequencynoise using a transformation is provided below:

/* FluidPotentialCorrector.h */ #ifndef FLUIDPOTENTIALCORRECTOR_H_(—)#define FLUIDPOTENTIALCORRECTOR_H_(—) #include<string> #include<vector>#include “RowSumData.h” #include “Mask.h” #include “RawImage.h” #include<cmath> #include <armadillo> class FluidPotentialCorrector { public:  // default constructor   // FluidPotentialCorrector( );   //constructor to set default scale factor   //FluidPotentialCorrector(const double scaleFactor);   // constructor toload file and set default scale factor  FluidPotentialCorrector(RawImage *raw, Mask *mask, const std::stringfileName, const double scaleFactor, const unsigned int startRow, constunsigned int endRow, const double noiseThresh);   // constructor forinitializing the object first and load files later  FluidPotentialCorrector(const double noiseThresh);   virtual~FluidPotentialCorrector( );   // load rowsum sensing electrode raw data  int loadSensingElectrodeData(const std::string fileName, unsigned intstartRow, unsigned int endRow);   // load rowsum sensing electrode rawdata   int loadSensingElectrodeDataThumbnail(const std::stringfileName,  const unsigned int numRows);   // set flag for signaling weare dealing with a thumbnail dataset   void setIsThumbnail( );   // setregion size   void setImage(RawImage *raw, Mask *mask, const unsignedint regionSizeRow, const unsigned int regionSizeCol, const charnucChar);   // perform fluid potential correction on whole image withregion size (regionXSize,   // regionYSize)   void doCorrection( );  void correctWithLastGoodFlow( );   void saveAverageFlowTraces( );   //perform fluid potential correction on wells within [rowStart, rowEnd)and   // [colStart, colEnd)   void applyScaleFactor(const unsigned introwStart, const unsigned int rowEnd, const unsigned int colStart, constunsigned int colEnd, const float scaleFactor, const std::vector<double>& senseTrace);   bool readRowSumIsSuccess( );   void setThreshold(constdouble threshold); private:   RawImage *raw;   Mask *mask;   charnucChar;   std::string rowsumFileName;   int readRowSumReturnValue;  double noiseThresh;   double scaleFactorDefault;   boolscaleFactorCorrection;   bool lastGoodFlowCorrection;   booluseDefaultScaleFactor;   bool correctSenseDrift;   unsigned intnumThumbnailRows;   unsigned int numThumbnailCols;   unsigned intnumThumbnailRegionsRow;   unsigned int numThumbnailRegionsCol;  RowSumData rowsum;   bool isThumbnail;   unsigned intnumRowsWholeChip;   unsigned int regionSizeRow, regionSizeCol;  std::vector<std::vector<float> > senseTrace;   std::vector<bool>senseTraceIsValid;   // std::vector<std::vector<std::vector<double> > >senseTraceAvgRegion;   std::map< char, std::vector< std::vector <std::vector < double > > > > lastGoodAvgTraces;   unsigned intThumbnailRow2wholeChipRow(const unsigned int row);   floatfindScaleFactor_fitSG(const float scaleFactorMin, const floatscaleFactorMax, const float scaleFactorBin, const unsigned int rowStart,const unsigned int rowEnd, const unsigned int colStart, const unsignedint colEnd, std::vector<double> & senseTraceAvg);   // adjust the offsetof trace to zero by zeroing the first numOffsetFrames frames   voidZeroTrace(std::vector<double> & trace, const unsigned intnumOffsetFrames);   // correct the drift of a trace by minimizing theleast square of the first   // numPointsStart data points in thebeginning and the last numPointsEnd data   // points at the end   voidCorrectTraceDrift(std::vector<double> & trace, const unsigned intnumPointsStart, const unsigned int numPointsEnd);   boolrowsumNoiseTooSmall( );   // convert a single trace first to variableframe compression (“vfc”) according to   // the block, then to uniform  void convertTraceUniformToThumbnail( std::vector<double> & trace,const unsigned int tn_region_row, const unsigned int tn_region_col);  std::vector<unsigned int> timeStampThumbnailRegionVFC(const unsignedint row, const unsigned int col);   std::vector<double>uniform2vfc(const std::vector<double> & trace, conststd::vector<unsigned int> & timeStamp, const std::vector<unsigned int> &timeStamp_vfc);   std::vector<double> vfc2thumbnail(conststd::vector<double> trace_vfc, const std::vector<unsigned int>timeStamp_vfc, const std::vector<unsigned int> timeStamps);   boolDEBUG;   std::vector<unsigned int> timeStamps; }; #endif /*FLUIDPOTENTIALCORRECTOR_H_ */

Further exemplary source code for removal of some or all high frequencynoise using a transformation is provided below:

FIG. 8 illustrates an example of fluid potential signal correction. Thex-axis represents time during sensing, expressed in seconds. The y-axisrepresents voltage, expressed in counts (which may be for practicalpurposes proportional to voltage). Curve 802 (see top curve with peaksbetween 2.5 and 3 seconds) depicts an original or uncorrected signal.Curve 804 (see smooth curve without peaks) depicts a corrected signal.Curve 806 (see bottom curve with peaks between 2.5 and 3 seconds)depicts the sensing electrode signal, which shows an electricaldisturbance in fluid potential that also affected the original signal.In this example, the signal may be averaged over all wells in athumbnail region (100 by 100 wells) and the scale factor α is 2.3.

In various embodiments, a signal corrected as discussed herein may thenbe further corrected for additional potential sources of errors or noise(e.g., background fitting or subtraction and/or phase effects). Forexample, a signal corrected as discussed herein may be furtherprocessed, modified, and/or corrected using the teachings of Davey etal., “Predictive Model for Use in Sequencing-by-Synthesis,” U.S. Pat.No. 8,666,678, issued Mar. 4, 2014; Rearick et al., “Models forAnalyzing Data from Sequencing-by-Synthesis Operations,” U.S. Pat. Appl.Publ. No. 2012/0172241, published Jul. 5, 2012; and Hubbell,“Time-Warped Background Signal for Sequencing-by-Synthesis Operations,”U.S. Pat. Appl. Publ. No. 2012/0173158, published Jul. 5, 2012, whichare all incorporated by reference herein in their entirety.

FIG. 9A illustrates an example of simulated injection of noise in asensing electrode signal. In this example, the noise may benumerically-injected, common-mode noise at a particular flow. The x-axisrepresents time during sensing, expressed in frames. The y-axisrepresents voltage, expressed in counts. Curve 902 (see sinusoidalcurve) depicts a curve representing the full noise time series withoutany variable frame compression. Curve 904 (see curve terminating shortlyafter 60 frames) depicts a curve representing the waveform aftervariable frame compression. Curve 906 (see curve with slope terminatingat about 0 counts) depicts a curve representing the waveform that wouldappear in thumbnail data having undergone a series of interpolation andextrapolation attempting to transform variable frame compression data tofull data. Such sensing electrode signals including simulated injectionof noise may be used to evaluate the effect of noise and the efficacy ofsignal correction.

FIG. 9B illustrates an example of simulated injection of noise in a wellsignal. In this example, the noise may be numerically-injected,common-mode noise at a particular flow. The x-axis represents timeduring sensing, expressed in frames. The y-axis represents voltage,expressed in counts. Curve 908 (see relatively smooth curve) representsan original waveform. Curve 910 (see curve with multiple peaks)represents the original waveform to which noise has been added. Suchwell signals including simulated injection of noise may be used toevaluate the effect of noise and the efficacy of signal correction.

FIGS. 10A and 10B illustrate examples of run statistics for a runincluding a relatively small amount of simulated noise. The runstatistics, as shown in FIG. 10A, may include mean read length 1002,median read length 1004, and mode read length 1006, along with ahistogram 1008 of read lengths. The run statistics, as shown in FIG.10B, may include mean raw accuracy 1010, and a plot 1012 of accuracy asa function of position in the read. In this example, the noise may be a200-count peak-to-peak noise. As may be seen in FIGS. 10A and 10B, therelatively small amount of simulated noise may have a minimal effect onthe run.

FIGS. 11A and 11B illustrate examples of run statistics for a runincluding a relatively large amount of simulated noise. The runstatistics, as shown in FIG. 11A, may include mean read length 1102,median read length 1104, and mode read length 1106, along with ahistogram 1108 of read lengths. The run statistics, as shown in FIG.11B, may include mean raw accuracy 1110, and a plot 1112 of accuracy asa function of position in the read. In this example, the noise may be a1,000-count peak-to-peak noise. As can be seen in FIGS. 11A and 11B, therelatively large amount of simulated noise may have a severe effect onthe run, including a severe drop 1114 in accuracy around position 50 anda lower mean raw accuracy of 98.4% (see FIG. 11B, compared with 98.8% inFIG. 10B).

FIGS. 12A and 12B illustrate run statistics and plots of error rates asa function of read position without correction for runs including arelatively large amount of simulated noise such as in FIGS. 11A and 11B.FIG. 12B shows total error rates (in curve 1202, see top curve),insertion error rates (in curve 1206, see second curve from the top),deletion error rates (in curve 1208, see third curve from the top), andmismatch error rates (in curve 1204, see bottom curve). Without thecorrection, there may be a severe drop 1210 in accuracy (see FIG. 12A)and increase in error rates 1212 (see FIG. 12B) around position 50.

FIGS. 13A and 13B illustrate run statistics and plots of error rates asa function of read position with correction for runs including arelatively large amount of simulated noise such as in FIGS. 11A and 11B.FIG. 13B shows total error rates (in curve 1302, see top curve),insertion error rates (in curve 1306, see second curve from the top),deletion error rates (in curve 1308, see third curve from the top), andmismatch error rates (in curve 1304, see bottom curve). With thecorrection as described herein with a scale factor α of 2.0 inferred byalgorithm matching the inserted noise magnitude, there may be no longera severe drop in accuracy (see FIG. 13A, compared with FIG. 12A) andincrease in error rates (see FIG. 13B, compared with FIG. 12B) aroundposition 50.

According to various exemplary embodiments, there may be provided amethod for correcting nucleotide incorporation signals for fluidpotential effects or disturbances arising in nucleic acidsequencing-by-synthesis, comprising: (a) disposing a plurality oftemplate polynucleotide strands in a plurality of defined spacesdisposed on a sensor array, at least some of the template polynucleotidestrands having a sequencing primer and a polymerase bound therewith; (b)exposing the template polynucleotide strands with the sequencing primerand a polymerase bound therewith to a series of flows of nucleotidespecies flowed according to a predetermined ordering through a fluidmanifold, the fluid manifold comprising passages for flowing nucleotidespecies and a branch passage for flowing a solution not comprisingnucleotide species, the branch passage comprising a reference electrodeand a sensing electrode; (c) obtaining a plurality of nucleotideincorporation signals corresponding to the plurality of defined spaces,the nucleotide incorporation signals having a signal intensity relatedto a number of nucleotide incorporations having occurred in thecorresponding defined space; and (d) correcting at least some of theplurality of nucleotide incorporation signals for fluid potentialeffects or disturbances using a mathematical transformation comprising ascale factor determined based on signals obtained from the sensingelectrode for each of a plurality of regions of defined spaces on thesensor array.

In such a method, correcting the at least some of the plurality ofnucleotide incorporation signals may comprise using an expressionw_(c)(t)=w(t)−αs (t), where w_(c)(t) represents a corrected sensorsignal, w(t) represents an uncorrected sensor signal, s(t) represents asensing electrode signal, and α represents the scale factor. Determiningthe scale factor may comprise selecting a fixed α as starting point.Determining the scale factor may further comprise calculating w_(c)(t)for each of a plurality of regions of defined spaces on the sensorarray. Determining the scale factor may further comprise calculating anaverage trace w_(c) (t) for the w_(c)(t) calculated for each of aplurality of regions of defined spaces on the sensor array to removenon-common-mode noise. Determining the scale factor may further comprisefitting w_(c) (t) with local polynomials. The local polynomials may bedetermined using a digital filter, such as a Savitzky-Golay filter, andmay be determined using a second order Savitzky-Golay filter.Determining the scale factor may further comprise calculating a meansquare error of w_(c) (t) from the fitting. Determining the scale factormay further comprise selecting the optimal scale factor α that minimizesthe mean square error.

According to various exemplary embodiments, there may be provided anon-transitory machine-readable storage medium comprising instructionswhich, when executed and/or implemented by a processor, cause theprocessor to perform a method for correcting nucleotide incorporationsignals for fluid potential effects or disturbances arising in nucleicacid sequencing-by-synthesis comprising (a) exposing a plurality oftemplate polynucleotide strands disposed in a plurality of definedspaces disposed on a sensor array and having a sequencing primer and apolymerase bound therewith to a series of flows of nucleotide speciesflowed according to a predetermined ordering through a fluid manifold,the fluid manifold comprising passages for flowing nucleotide speciesand a branch passage for flowing a solution not comprising nucleotidespecies, the branch passage comprising a reference electrode and asensing electrode; (b) obtaining a plurality of nucleotide incorporationsignals corresponding to the plurality of defined spaces, the nucleotideincorporation signals having a signal intensity related to a number ofnucleotide incorporations having occurred in the corresponding definedspace; and (c) correcting at least some of the plurality of nucleotideincorporation signals for fluid potential effects or disturbances usinga mathematical transformation comprising a scale factor determined basedon signals obtained from the sensing electrode for each of a pluralityof regions of defined spaces on the sensor array.

In such a non-transitory machine-readable storage medium, correcting theat least some of the plurality of nucleotide incorporation signals maycomprise using an expression w_(c) (t)=w(t)−αs(t), where w_(c) (t)represents a corrected sensor signal, w(t) represents an uncorrectedsensor signal, s(t) represents a sensing electrode signal, and αrepresents the scale factor. Determining the scale factor may compriseselecting a fixed α as starting point. Determining the scale factor mayfurther comprise calculating w_(c) (t) for each of a plurality ofregions of defined spaces on the sensor array. Determining the scalefactor may further comprise calculating an average trace w_(c) (t) forthe w_(c)(t) calculated for each of a plurality of regions of definedspaces on the sensor array to remove non-common-mode noise. Determiningthe scale factor may further comprise fitting w_(c) (t) with localpolynomials. The local polynomials may be determined using a digitalfilter, such as a Savitzky-Golay filter, and may be determined using asecond order Savitzky-Golay filter. Determining the scale factor mayfurther comprises calculating a mean square error of w_(c) (t) from thefitting. Determining the scale factor may further comprises selectingthe optimal scale factor α that minimizes the mean square error.

In various embodiments, general sequencing-by-synthesis aspects relatingto the present disclosure may comprise one or more features described inRothberg et al., U.S. Pat. No. 7,948,015, and Rothberg et al., U.S. Pat.Appl. Publ. Nos. 2010/0137143, 2009/0026082, and 2010/0282617, which areall incorporated by reference herein in their entirety.

In various embodiments, nucleic acid sequencing data compression aspectsrelating to the present disclosure may comprise one or more featuresdescribed in Sugnet et al., U.S. Pat. Appl. Publ. No. 2013/0231870,published Sep. 5, 2013, which is incorporated by reference herein intheir entirety.

In various embodiments, base calling aspects relating to the presentdisclosure may include performing or implementing one or more of theteachings disclosed in Davey et al., U.S. Pat. No. 8,666,678, issuedMar. 4, 2014, which is incorporated by reference herein in its entirety.Other aspects of signal processing and base calling may includeperforming or implementing one or more of the teachings disclosed inDavey et al., U.S. Pat. Appl. Publ. No. 2012/0173159, published Jul. 5,2012, and Sikora et al., U.S. Pat. Appl. Publ. No. 2013/0060482,published Mar. 7, 2013, which are all incorporated by reference hereinin their entirety.

In various embodiments, flow ordering aspects relating to the presentdisclosure may comprise one or more features described in Hubbell etal., U.S. Pat. Appl. Publ. No. 2012/0264621, published Oct. 18, 2012,which is incorporated by reference herein in its entirety.

FIGS. 14A and 14B illustrate error rates and coverage depth for runswithout (FIG. 14A) and with (FIG. 14B) fluid potential artifactcorrection. FIG. 14A shows data for a user-compromised run affected byan elevated error rate due to a user touching tubings. FIG. 14B showsthe same, after correction for fluid potential artifact. The x-axisrepresents the base position. The y-axis represents the error rate (onthe left) and coverage depth (on the right). Shown are coverage depthcurves 1402 a and 1402 b (see curves starting in the upper left cornerof the plots). Also shown are total error rates (in curves 1404 a and1404 b, see top curves), insertion error rates (in curves 1406 a and1406 b, see second curves from the top), deletion error rates (in curves1408 a and 1408 b, see third curves from the top), and substitutionerror rates (in curves 1410 a and 1410 b, see bottom curves). Withoutthe correction, there is a significant increase in error rate (seeregion 1412 of FIG. 14A between positions 150 and 200 and compare withFIG. 14B). Also, the total error rate was 1.2% with 66.3 millionhigh-quality (Q20) bases in FIG. 14A compared to 1.1% with 68 millionhigh-quality (Q20) bases in FIG. 14B.

In various embodiments, fluid potential artifact correction methods,systems, and non-transitory machine-readable storage media may reduce atotal error rate in a user-compromised run by about 0.1% (in absolutepercentage value), which represents a relative reduction in total errorrate expressed in absolute percentage value of about(|1.1%−1.2%|)/1.2%=0.08333333 or about 8.3%. In addition, fluidpotential artifact correction methods, systems, and non-transitorymachine-readable storage media may increase a number of high-quality(Q20) bases in a user-compromised run by about 1.7 million (in absolutenumber of bases), which represents a relative augmentation inhigh-quality (Q20) bases of about (|68−66.3|)/66.3=0.0256410 or about2.6%. It should be noted, however, that error rate and number ofhigh-quality (Q20) bases depend on numerous factors and experimentconditions, which may otherwise affect accuracy and in some cases may bemore significant than fluid potential artifacts.

According to various embodiments, some errors related to disturbances influid potential may be corrected using a sensing electrode andmathematical transformation as described herein. It should be noted,however, that this correction approach may not correct all sources oferror. In some embodiments, various fluid potential correctionembodiments as described herein may be combined with other signalcorrection algorithms addressing other sources of error (e.g.,background effects or other distortion effects).

FIGS. 15A and 15B illustrate examples of simultaneous measurementsshowing different response across columns for a non-common mode noise.The x-axis represents time during sensing, expressed in frames. They-axis represents voltage, expressed in counts. Shown in each of FIGS.15A and 15B are average live traces for a thumbnail row region (e.g.,100 by 100 wells) for 12 columns (see curves of column portions 1502 aand 1502 b) and the sensor electrode (see curves 1504 a and 1504 b). Thenoise here may be due to electrical noise induced by bubbles blockingsome wells. Traces differ significantly depending on the row region (andacross columns one can note some outlier traces for a given row region).

FIGS. 16A and 16B illustrate examples of a spatial distribution of errorrates for a non-common mode noise after a flow resulting in significanterrors. The x-axis and y-axis of FIG. 16A represent length along twosides of a sensor, with each block corresponding to a region of sensorson a chip. As shown in FIG. 16A, the blocks have a heterogenerousshading throughout many of the regions of the sensors on the chip. Ascan be seen, errors (see regions 1602 of FIG. 16A) appear the blocks inadjacent regions that have a homogenous shading. These error also may bemostly associated with a small number of regions, which tend to be alongthe periphery of the array of regions. Further analysis may have shownthat these regions have non-common mode noise that cannot be removedusing a sensing electrode and correction method as described herein.FIG. 16B illustrates an example of the spatial distribution of errorrates of FIG. 16A in a bar graph, where the x-axis of FIG. 16Brepresents the error rate and the y-axis of FIG. 16B represents thefrequency counts.

FIGS. 17A and 17B illustrate examples of a spatial distribution of errorrates for a non-common mode noise after a flow not resulting insignificant errors. The x-axis and y-axis of FIG. 17A represent lengthalong two sides of a sensor, with each block corresponding to a regionof sensors on a chip. As shown in FIG. 17A, the blocks have aheterogenerous shading throughout the regions of the sensors on thechip. FIG. 17B illustrates an example of the spatial distribution oferror rates of FIG. 17A in a bar graph, where the x-axis of FIG. 17Brepresents the error rate and the y-axis of FIG. 17B represents thefrequency counts. As can be seen by comparing the FIG. 16A to FIG. 17Aand FIG. 16B to FIG. 17B, the errors shown in FIGS. 17A and 17B wererelatively rare in this case, allowing a baseline comparison with FIGS.16A and 16B.

FIG. 18 illustrates an exemplary computer system. The computer system1801 may include a bus 1802 or other communication mechanism forcommunicating information, a processor 1803 coupled to the bus 1802 forprocessing information, and a memory 1805 coupled to the bus 1802 fordynamically and/or statically storing information. The computer system1801 can also include one or more co-processors 1804 coupled to the bus1802, such as GPUs and/or FPGAs, for performing specialized processingtasks; a display 1806 coupled to the bus 1802, such as a cathode raytube (“CRT”) and/or liquid crystal display (“LCD”), for displayinginformation to a computer user; an input device 1807 coupled to the bus1802, such as a keyboard including alphanumeric and other keys, forcommunicating information and command selections to the processor 1803;a cursor control device 1808 coupled to the bus 1802, such as a mouse, atrackball, and/or cursor direction keys for communicating directioninformation and command selections to the processor 1803 and forcontrolling cursor movement on display 1806; and one or more storagedevices 1809 coupled to the bus 1802, such as a solid state drive, ahard disk drive, a magnetic disk, and/or an optical disk, for storinginformation and instructions. The memory 1805 may include a randomaccess memory (“RAM”) or other dynamic storage device and/or a read onlymemory (“ROM”) or other static storage device. Such an exemplarycomputer system with suitable software may be used to perform theembodiments described herein. More generally, in various embodiments,one or more features of the teachings and/or embodiments describedherein may be performed or implemented using appropriately configuredand/or programmed hardware and/or software elements.

Examples of hardware elements may include processors, microprocessors,input(s) and/or output(s) (“I/O”) device(s) (or peripherals) that arecommunicatively coupled via a local interface circuit, circuit elements(e.g., transistors, resistors, capacitors, inductors, and so forth),integrated circuits, application specific integrated circuits (“ASIC”),programmable logic devices (“PLD”), digital signal processors (“DSP”),field programmable gate array (“FPGA”), logic gates, registers,semiconductor device, chips, microchips, chip sets, and so forth. Thelocal interface may include, for example, one or more buses or otherwired or wireless connections, controllers, buffers (caches), drivers,repeaters and receivers, etc., to allow appropriate communicationsbetween hardware components. A processor is a hardware device forexecuting software, particularly software stored in memory. Theprocessor can be any custom made or commercially available processor, acentral processing unit (“CPU”), an auxiliary processor among severalprocessors associated with the computer, a semiconductor basedmicroprocessor (e.g., in the form of a microchip or chip set), amacroprocessor, or generally any device for executing softwareinstructions. A processor can also represent a distributed processingarchitecture. The I/O devices can include input devices, for example, akeyboard, a mouse, a scanner, a microphone, a touch screen, an interfacefor various medical devices and/or laboratory instruments, a bar codereader, a stylus, a laser reader, a radio-frequency device reader, etc.Furthermore, the I/O devices also can include output devices, forexample, a printer, a bar code printer, a display, etc. Finally, the I/Odevices further can include devices that communicate as both inputs andoutputs, for example, a modulator/demodulator (modem; for accessinganother device, system, or network), a radio frequency (“RF”) or othertransceiver, a telephonic interface, a bridge, a router, etc.

Examples of software may include software components, programs,applications, computer programs, application programs, system programs,machine programs, operating system software, middleware, firmware,software modules, routines, subroutines, functions, methods, procedures,software interfaces, application program interfaces (“API”), instructionsets, computing code, computer code, code segments, computer codesegments, words, values, symbols, or any combination thereof. A softwarein memory may include one or more separate programs, which may includeordered listings of executable instructions for implementing logicalfunctions. The software in memory may include a system for identifyingdata streams in accordance with the present teachings and any suitablecustom made or commercially available operating system (“O/S”), whichmay control the execution of other computer programs such as the system,and provides scheduling, input-output control, file and data management,memory management, communication control, etc.

According to various embodiments, one or more features of teachingsand/or embodiments described herein may be performed or implementedusing an appropriately configured and/or programmed non-transitorymachine-readable medium or article that may store an instruction or aset of instructions that, if executed by a machine, may cause themachine to perform a method and/or operations in accordance with theembodiments. Such a machine may include, for example, any suitableprocessing platform, computing platform, computing device, processingdevice, computing system, processing system, computer, processor,scientific or laboratory instrument, etc., and may be implemented usingany suitable combination of hardware and/or software. Themachine-readable medium or article may include, for example, anysuitable type of memory unit, memory device, memory article, memorymedium, storage device, storage article, storage medium and/or storageunit, for example, memory, removable or non-removable media, erasable ornon-erasable media, writeable or re-writeable media, digital or analogmedia, hard disk, floppy disk, read-only memory compact disc (“CD-ROM”),recordable compact disc (“CD-R”), rewriteable compact disc (“CD-RW”),optical disk, magnetic media, magneto-optical media, removable memorycards or disks, various types of Digital Versatile Disc (“DVD”), a tape,a cassette, etc., including any medium suitable for use in a computer.Memory can include any one or a combination of volatile memory elements(e.g., random access memory (“RAM”, such as DRAM, SRAM, SDRAM, etc.))and nonvolatile memory elements (e.g., ROM, EPROM, EEROM, Flash memory,hard drive, tape, CD-ROM, etc.). Moreover, memory can incorporateelectronic, magnetic, optical, and/or other types of storage media.Memory can have a distributed, clustered, remote, or cloud architecturewhere various components are situated remote from one another, but arestill accessed by the processor. The instructions may include anysuitable type of code, such as source code, compiled code, interpretedcode, executable code, static code, dynamic code, encrypted code, etc.,implemented using any suitable high-level, low-level, object-oriented,visual, compiled and/or interpreted programming language.

Unless otherwise specifically designated herein, terms, techniques, andsymbols of biochemistry, cell biology, genetics, molecular biology,nucleic acid chemistry, nucleic acid sequencing, and organic chemistryused herein follow those of standard treatises and texts in the relevantfield.

Although the present description described in detail certainembodiments, other embodiments are also possible and within the scope ofthe present invention. For example, those skilled in the art mayappreciate from the present description that the present teachings maybe implemented in a variety of forms, and that the various embodimentsmay be implemented alone or in combination. Variations and modificationswill be apparent to those skilled in the art from consideration of thespecification and figures and practice of the teachings described in thespecification and figures, and the claims.

1.-12. (canceled)
 13. An apparatus comprising: a flow cell including afluid inlet and a fluid outlet; an array of electronic sensorscooperatively engaged with the flow cell, each of the electronic sensorsincluding a field effect transistor having a gate electrode, wherein afirst subset of the array of electronic sensors is exposed to a fluidwithin the flow cell, and a second subset of the array of electronicsensors is free of contact with the fluid within the flow cell; and asensor electrode in electrical communication with the first subset ofthe array of electronic sensors through fluid within at least one of thefluid inlet and the fluid outlet, wherein the sensor electrode has anoutput in electrical communication with the gate electrodes of the fieldeffect transistors of the second subset of the array of electronicsensors.
 14. The apparatus of claim 13, wherein the array of electronicsensors is arranged in rows and columns, and wherein the second subsetof the array of electronic sensors includes a column of electronicsensors, the output of the sensor electrode in electrical communicationwith the each electronic sensor within the column of electronic sensorsof the second subset of the array of electronic sensors.
 15. Theapparatus of claim 13, further comprising: a fluid manifold in fluidcommunication with a plurality of reagent reservoirs, the fluid manifoldincluding an outlet passage in fluid communication with the fluid inlet,wherein the sensor electrode being in electrical communication with thesecond subset of the array of electronic sensors through a solutionwithin the outlet passage.
 16. The apparatus of claim 15, furthercomprising: a branch passage between the fluid manifold and the flowcell in fluid communication with the outlet passage, wherein the sensorelectrode is disposed in the branch passage.
 17. The apparatus of claim16, further comprising: a reference electrode to provide a referencevoltage to the first subset of the array of electronic sensors through asolution via the fluid inlet or the fluid outlet, wherein the referenceelectrode is disposed in contact with fluid within the branch passage.18. The apparatus of claim 15, further comprising: a reference electrodeto provide a reference voltage to the first subset of the array ofelectronic sensors through a solution via the fluid inlet or the fluidoutlet, wherein the plurality of reagent reservoirs include a pluralityof reagents, and wherein the reference electrode is free of directcontact with one or more reagents of the plurality of reagents when theone or more reagents flows through the outlet passage. 19.-23.(canceled)
 24. The apparatus of claim 13, further comprising: areference electrode to provide a reference voltage to the first subsetof the array of electronic sensors through a solution via the fluidinlet or the fluid outlet.
 25. The apparatus of claim 13, furthercomprising: an array of wells providing fluid access to the gateelectrodes of the field effect transistors of the first subset of thearray of electronic sensors.
 26. The apparatus of claim 13, furthercomprising: an amplifier disposed in electrical communication betweenthe output of the sensor electrode and the gate electrodes of the fieldeffect transistors of the second subset of the array of electronicsensors.
 27. The apparatus of claim 13, wherein the field effecttransistors of the first subset of the array of electronic sensorsinclude ion sensitive field effect transistors. 28.-35. (canceled)
 36. Amethod for measuring a reaction product, the method comprising: flowinga reagent solution into a flow cell in fluid communication with an arrayof electronic sensors cooperatively engaged with the flow cell, whereina first subset of the array of electronic sensors is exposed to thereagent solution within the flow cell, a second subset of the array ofelectronic sensors is free of contact with the reagent solution withinthe flow cell, and wherein the reagent solution reacts to provide areaction product; measuring a first response of the first subset of thearray of electronic sensors to the reaction product; measuring a secondresponse of the second subset of the array of electronic sensors, thesecond subset of the array of electronic sensors in electricalcommunication with a sensor electrode in fluid communication with theflow cell; and adjusting the first response of the first subset of thearray of electronic sensors based on the second response of the secondsubset of the array of electronic sensors.
 37. The method of claim 36,wherein each of the electronic sensors includes a field effecttransistor having a gate electrode; and wherein the sensor electrode isin electrical communication with the first subset of the array ofelectronic sensors through fluid, an output of the sensor electrode inelectrical communication with the gate electrodes of the field effecttransistors of the second subset of the array of electronic sensors. 38.The method of claim 36, wherein the array of electronic sensors isarranged in rows and columns, and wherein the second subset of the arrayof electronic sensors includes a column of electronic sensors, an outputof the sensor electrode in electrical communication with the eachelectronic sensor within the column of electronic sensors of the secondsubset of the array of electronic sensors.
 39. The method of claim 36,further comprising: applying a reference voltage through a solution influid communication with the flow cell in fluid communication with thefirst subset of the array of electronic sensors.
 40. The method of claim39, wherein the reference voltage is applied by a reference electrode.41. The method of claim 36, wherein the array of electronic sensorsincludes field effect transistors.
 42. The method of claim 41, whereinthe field effect transistors include ion sensitive field effecttransistors.
 43. The method of claim 36, further comprising: flowing asolution through the sensor electrode; measuring a third response of thesensor electrode through the solution; and amplifying the third responseof the sensor electrode.
 44. The method of claim 43, further comprising:providing an offset to the third response of the sensor electrode tocenter the third response relative to a reference voltage.
 45. Themethod of claim 36, wherein the first response of the first subset ofthe array of electronic sensors is adjusted by scaling and subtractingthe second response of the second subset of the array of electronicsensors.
 46. A method for correcting nucleotide incorporation signalsfor fluid potential effects or disturbances arising in nucleic acidsequencing-by-synthesis, comprising: disposing a plurality of templatepolynucleotide strands in a plurality of defined spaces disposed on asensor array, at least some of the plurality of template polynucleotidestrands having a sequencing primer and a polymerase bound therewith;exposing the at least some of the plurality of template polynucleotidestrands with the sequencing primer and a polymerase bound therewith to aseries of flows of nucleotide species flowed according to apredetermined ordering through a fluid manifold, the fluid manifoldcomprising passages for flowing the series of flows of the nucleotidespecies and comprising a branch passage for flowing a solution notcomprising the nucleotide species, the branch passage comprising areference electrode and a sensing electrode; obtaining a plurality ofnucleotide incorporation signals corresponding to the plurality ofdefined spaces, the nucleotide incorporation signals having a signalintensity related to a number of nucleotide incorporations havingoccurred in the corresponding defined space; and correcting at leastsome of the plurality of nucleotide incorporation signals for fluidpotential effects or disturbances using a mathematical transformationcomprising a scale factor determined based on signals obtained from thesensing electrode for each of a plurality of regions of defined spaceson the sensor array.
 47. The method of claim 46, wherein correcting theat least some of the plurality of nucleotide incorporation signalscomprises using an expression w_(c)(t)=w(t)−αs(t), where w_(c)(t)represents a corrected sensor signal, w(t) represents an uncorrectedsensor signal, s(t) represents a sensing electrode signal, and αrepresents the scale factor.
 48. The method of claim 47, whereindetermining the scale factor comprises: selecting a fixed α as astarting point.
 49. The method of claim 48, wherein determining thescale factor further comprises: calculating w_(c)(t) for each of aplurality of regions of defined spaces on the sensor array.
 50. Themethod of claim 49, wherein determining the scale factor furthercomprises: calculating an average trace w_(c) (t) for the w_(c) (t)calculated for each of a plurality of regions of defined spaces on thesensor array to remove non-common-mode noise.
 51. The method of claim50, wherein determining the scale factor further comprises: fittingw_(c) (t) with local polynomials.
 52. The method of claim 51, whereinthe local polynomials are determined using a Savitzky-Golay filter. 53.The method of claim 51, wherein the local polynomials are determinedusing a second order Savitzky-Golay filter.
 54. The method of claim 51,wherein determining the scale factor further comprises: calculating amean square error of w_(c) (t) from the fitting.
 55. The method of claim54, wherein determining the scale factor further comprises: selectingthe optimal scale factor α that minimizes the mean square error. 56.-65.(canceled)